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What is space ?
We define space as an area which has neither gravitational force
nor the friction. Space is the boundless three-dimensional extent
in which objects and events have relative position and
direction. Physical space is often conceived in three linear
dimensions, although modern physicists usually consider it,
with time, to be part of a boundless four-
dimensional continuum known as space time .The concept of
space is considered to be of fundamental importance to an
understanding of the physical universe. However, disagreement
continues between philosophers over whether it is itself an entity,
a relationship between entities, or part of a conceptual framework

Angular Distance Between Two Points on a Sphere

Finding the angular distance between two points on a
sphere of radius R , suppose that the two points
have a right ascension (RA) of ϕ1 and ϕ2, and a
declination (DEC) of and . Alternatively, the
angles ϕ and could correspond to geographical
longitude and latitude respectively. The angle at the
center of the sphere separating the two points is:
The arc length on the spherical surface is equal to the
radius of the sphere times (in radians). When
the two points are extremely close together (or
otherwise when is close to unity),
different formulas must be used to ensure sufficient
precision .
1 2

  21cos2cos1cos2sin1sinarccos  

cos

Uses of this
formula
▪ The main use of this formula is
to measure the distance
between two points in planet
without entering into that
planet.

Blackbody Radiation Spectrum,
Planck Function

The Blackbody radiation spectrum, or Planck function,
can be expressed in a number of ways. There are
various choices of units but we use examples with a
specific set of units in order to clearly illustrate the
physical nature of each function. The
notation B denotes the intensity spectrum (per unit
solid angle), and the notation u donates the energy
density (energy per unit volume). The energy
density is related to the intensity simply by
multiplying the latter by 4π/c for isotropic
radiation, summed over all directions. However, if we
are dealing with a general angular distribution of
radiation we have to start with the energy density
per unit solid angle, in which case we would multiply
by 1/c instead of 4π/c. We would then integrate
over solid angle.
134 
 cmcmB
c
uE 


The above formula we can write in different ways:
▪ In terms of frequency using some of this formula
▪ In terms of wavelength
▪ In terms of energy:
13
2
4 
 cmcmB
hc
u 

134 
 HzcmB
c
u vv

134 
 ergcmB
cE
u EE
 2




cd
dv
C
v
vc
hdvdE
hvE






For the blackbody spectrum or
Planck function formulas
▪ In terms of frequency
▪ In terms of wavelength
▪ In terms of energy
1112
2
3
1)/exp(
12 

 steradianHzsergcm
kThvc
hv
Bv
1112
5
2
1)/exp(
12 

 steradiancmsergcm
kThc
hc
B


1112
32
3
1)/exp(
12 

 steradianergsergcm
kTEhc
E
BE

In space means in 3D we denote center of mass as
where :
▪
▪ In this way all the coordinates will form.
),,( zyxCM
M
xm
m
xm
x nn
n
nn 




M
xm
m
xm
x nn
n
nn 





hourmiles
r
AU
M
M
v /
1
94200
2/12/1














r
r
c
v g2

km
M
M
r
cmMr
where
g
g









4822.1
104822.1 8
13







r
GM
v
2

In layman's terms, it is defined as "the
point of no return", i.e., the point at
which the gravitational pull becomes so
great as to make escape impossible, even
for light.

An event horizon is most commonly associated
with black holes. Light emitted from inside the event
horizon can never reach the outside observer. For a
non-spinning (stationary) black hole , the event horizon
radius, , is the location (radius) from the center of
the black hole for which light originating at radii less
than the horizon radius cannot escape to infinity
because it would be subject to an infinite red shift.
The event horizon radius in this case is synonymous
with the Schwarzschild radius.
hR

Where a is the dimensionless angular momentum of the black hole,
lying between 0 and 1, and is the gravitational radius.
 2
11 a
R
R
g
h

gR

A radius definedfor a bodyof a givenmass
and proportional to that mass, such that if
the bodyis smallerthan that radius, the
force of gravityis strongenoughto prevent
matter andenergyto escape fromwithin
that radius.

where
G is the gravitational constant,
M is the black-hole mass, and
c is the speed of light.
2
c
GM
rg 
cmMrg 8
3
104822.1 

In the simplest case, if the radiation source is isotropic and has a total luminosity
of L (in say, erg s−1), and the flux measured at a distance r from the source
is F (in say, erg cm−2 s−1), then the surface area of the sphere times the flux
must be equal to the total luminosity (power) at any distance (all r) from the
source:
4πr2F = L
Then
F = L4πr2
and the latter is the inverse square law. The same basic relation applies if instead
of L we have the total number of photons s−1 emitted isotropic ally in all
directions, say N0, and instead of F we have the number of
photons s−1intercepted per unit area at some distance r from the source,
say n(r). That would give the following formula (using concrete units to make it
even more clear):
    
2
12
4
/
r
sphotonsN
sphotonscmrn o



3. Kepler’s Third
Law
The square of the
orbital period of
a planet in orbit
around the sun is
proportional to
the cube of the
semi major axis
of the orbit.
(The semi major
axis is equal to
half of the
largest symmetry
axis of the ellipse

It has been obvious for a long
while that the motions of galaxies
in groups and clusters, if simply
interpreted, imply the existence
of a substantial amount of mass in
addition to that traditionally
associated with individual galaxies

FORMULASFOR LIGHT CROSSING TIMES
1. where r = is the distance.
2. t∼500(r1AU) seconds , Here r = is in astronomical units (AU)
3. Light-crossing time per gravitational radius:
c
r
t 
ondsM
c
r
t
g
sec500~ 8







Orbital mechanics or
astrodynamics is the
application of ballistics and
celestial mechanics to the
practical problems
concerning the motion of
rocket and other spacecraft

hourmiles
r
AU
M
M
v
skm
r
AU
M
M
v
r
GM
v
/
1
66600~
/
1
30~
2/12/1
2/12/1

































r
r
c
v g

2/1
2 






a
r
v
v
f
circular
elliptical
elliptical

In general, two masses, m and Mwill orbit around
the center of mass of the systemand the systemcan
be replacedby the motionof the reduced
mass, μ≡mM/(m+M). It is important to
understandthat the following equationsare valid
for elliptical orbits(i.e., not just circular), and for
arbitrary masses (i.e., not just for the case for one
massmuch lessthanthe other). Theonly
restrictionis that the motionis purely dueto
gravity and that the motionin nonrelativistic .
 
2/13
2 







mMG
a
T 

 
  
2/13








mMsesinsolarmas
a
yearT AU
a AU is the semi major axis in units of AU.

1. The effect whereby
the position or direction
of an object appears to
differ when viewed from
different positions, e.g.
through the viewfinder
and the lens of a
camera.
2. The angular amount of
parallax in a particular
case, especially that of
a star viewed from
different points in the
earth's orbit.

pc
ondsarcparallax
d
d
x
)sec(
1
sin~~~tan



The Schwarzschild radius of a
black hole is the location of
the event horizon from the
center of a non-spinning
(stationary) black hole. In
other words, light originating
at radii less than the
Schwarzschild radius cannot
escape to infinity because it
would be subject to an infinite
red shift.

AUM
M
M
R
cmMR
km
M
M
R
km
M
M
R
c
GM
R
s
s
s
s
s
88
8
13
2
2
10
2~
109644.2
3~
9644.2
2























